Contribution of the irreversible displacement of domain walls to the piezoelectric effect in barium titanate and lead zirconate titanate ceramics

The contribution from the irreversible displacement of non-180 degrees domain walls to the direct longitudinal piezoelectric d(33) coefficient of BaTiO3 and Pb(Zr,Ti)O-3 ceramics was determined quantitatively by using the Rayleigh law. Effects of the crystal structure and microstructure of the ceramics as well as the external d.c. pressure on the domain wall contribution to d(33) were examined. In barium titanate, this domain wall contribution is large (up to 35% of the total d(33), under the experimental conditions used) and dependent on the external d.c. pressure in coarse grained ceramics, and much smaller and independent of the external d.c. pressure in fine-grained samples. The presence of internal stresses in fine-grained ceramics could account for the observed behaviour. The analysis shows that the domain-wall contribution to the d(33) in lead zirconate titanate ceramics is large in compositions close to the morphotropic phase boundary that contain a mixture of tetragonal and rhombohedral phases, and in rhombohedral compositions (up to 40% of the total d(33)). The domain-wall contribution to the piezoelectric response from the irreversible displacement of domain walls is significantly smaller in tetragonal Pb(Zr,Ti)O-3 samples where it decreases with increasing spontaneous strain.